The CES framework has potential for both the calibration and uncertainty quantification of comprehensive climate models, and other computationally expensive models. It is computationally efficient enough to use data averaged in time (e.g., over seasons), which need to be accumulated over longer model runs. Time-averaged climate statistics, including mean values and higher-order statistics such as extreme value statistics, are what typically matters in climate predictions. CES allows us to focus model calibration and uncertainty quantification on such immediately relevant statistics. Using time averaged statistics also has the advantage that it leads to smoother, albeit still noisy, objective functions when compared with calibration of climate models by minimizing mismatches in instantaneous, short-term forecasts [1]}. The latter approach can improve short-term forecasts but may not translate into improved climate simulations [2]}. It also suffers from the difficulty that model resolution and data resolution may be mismatched. Focusing on climate statistics, as we did in our proof-of-concept here, circumvents this problem: time-aggregated climate statistics are varying relatively smoothly in space and, hence, minimizing mismatches in statistics between models and data does not suffer from the resolution-mismatch problem. CES can be used to learn about arbitrary parameters in climate models from time-averaged data. It leads to quantification of parametric uncertainties that then can be converted into parametric uncertainties in predictions by sampling from the posterior distribution of parameters.
